Question

Candidates of four schools appear in a mathematics test. The data were as follows:
If the average score of the candidates of all the four schools is 66, find the number of candidates that appeared from school III.
schools No.of candidates Average Score
I 60 75
II 48 80
III Not Available 55
IV 40 50

Answer 1

No. of candidates in school III are 52

•let no. of candidates from school III are x

•No. of candidates from school

I:II:III:IV are 60:48:x:40

• Their respective avg. are

75:80:55:50

• overall average score = sum of total score by each school /total no. of students

• 66 =

(4500+3840+55x+2000)/(148+x)

• cross multiplying

66(148+x)= 10340 +55x

• 9768 +66x = 10340 +55x

• 11x = 572

• x=52

Answer 2

52 Students in School III

Step-by-step explanation:

Let say number of Students appeared from school III = S

School     Number of students    Average Socre    students * average

I                     60                               75                      4500

II                    48                               80                      3840

III                   S                                 55                       55S

IV                  40                               50                      2000

Total            148 + S                                                   10340 + 55S

Average Score  = ( 10340 + 55S)/(148 + S)

( 10340 + 55S)/(148 + S) = 66

=> 10340 + 55S = 9768 + 66S

=> 11S = 572

=> S = 52

52 Students in School III

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